Question: 7 people can paint 6 walls in 49 minutes. How many minutes will it take for 8 people to paint 9 walls? Round to the nearest minute.
Explanation: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 6\text{ walls}\\ p &= 7\text{ people}\\ t &= 49\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{6}{49 \cdot 7} = \dfrac{6}{343}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 9 walls with 8 people. $t = \dfrac{w}{r \cdot p} = \dfrac{9}{\dfrac{6}{343} \cdot 8} = \dfrac{9}{\dfrac{48}{343}} = \dfrac{1029}{16}\text{ minutes}$ $= 64 \dfrac{5}{16}\text{ minutes}$ Round to the nearest minute: $t = 64\text{ minutes}$